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Timed Shuffle Expressions

  • Cătălin Dima
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3653)

Abstract

We show that stopwatch automata are equivalent to timed shuffle expressions, an extension of timed regular expressions with the shuffle operation. This implies that the emptiness problem for timed shuffle expressions is undecidable. The result holds for both timed state sequence semantics and timed event sequence semantics of automata and expressions.

Similarly to timed regular expressions, our timed shuffle expressions employ renaming. But we show that even when renaming is not used, shuffle regular expressions still have an undecidable emptiness problem. This solves in the negative a conjecture of Asarin on the possibility to use shuffle to define timed regular languages.

Keywords

Regular Expression Regular Language Discrete Transition Action Semantic State Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Asarin, E.: Challenges in timed languages. Bulletin of EATCS 83 (2004) Google Scholar
  3. 3.
    Asarin, E., Caspi, P., Maler, O.: A Kleene theorem for timed automata. In: Proceedings of LICS 1997, pp. 160–171 (1997)Google Scholar
  4. 4.
    Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. Journal of ACM 49, 172–206 (2002)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Bouyer, P., Petit, A.: Decomposition and composition of timed automata. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, p. 210. Springer, Heidelberg (1999)Google Scholar
  6. 6.
    Dima, C.: Kleene theorems for event-clock automata. In: Ciobanu, G., Păun, G. (eds.) FCT 1999. LNCS, vol. 1684, pp. 215–225. Springer, Heidelberg (1999)Google Scholar
  7. 7.
    Dima, C.: Real-time automata. Journal of Automata, Languages and Combinatorics 6, 3–23 (2001)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Dima, C.: A nonarchimedian discretization for timed languages. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, pp. 161–181. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata. J. Comput. Syst. Sci 57, 94–124 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Herrmann, P.: Renaming is necessary in timed regular expressions. In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 47–59. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  11. 11.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley/Narosa Publishing House (1992)Google Scholar
  12. 12.
    Krcál, P., Yi, W.: Decidable and undecidable problems in schedulability analysis using timed automata. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 236–250. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Ouaknine, J., Worrell, J.: Revisiting digitization, robustness, and decidability for timed automata. In: Proceedings of LICS 2003, pp. 198–207. IEEE Computer Society Press, Los Alamitos (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Cătălin Dima
    • 1
  1. 1.Laboratoire d’Algorithmique, Complexité et LogiqueUniversité Paris XIICréteil CedexFrance

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